# ELATE: Elastic tensor analysis

Welcome to ELATE, the online tool for analysis of elastic tensors, developed by **Romain Gaillac** and **François-Xavier Coudert** at CNRS / Chimie
ParisTech.

If you use the software in published results (paper, conference, etc.), please cite the corresponding paper (*J. Phys. Condens. Matter*, 2016, 28, 275201) and give the
website URL.

ELATE is open source software. Any queries or comments are welcome at

## Summary of the properties

### Input: stiffness matrix (coefficients in GPa) of SmFe5 (Materials Project id mp-1566)

169 59 75 0 0 -2 59 175 74 0 0 -2 75 74 239 0 0 1 0 0 0 67 0 0 0 0 0 0 68 0 -2 -2 1 0 0 56

### Average properties

Averaging scheme | Bulk modulus | Young's modulus | Shear modulus | Poisson's ratio |
---|---|---|---|---|

Voigt | K_{V} = 111 GPa | E_{V} = 159.36 GPa | G_{V} = 63.2 GPa | ν_{V} = 0.26073 |

Reuss | K_{R} = 107.26 GPa | E_{R} = 156.45 GPa | G_{R} = 62.238 GPa | ν_{R} = 0.2569 |

Hill | K_{H} = 109.13 GPa | E_{H} = 157.91 GPa | G_{H} = 62.719 GPa | ν_{H} = 0.25884 |

### Eigenvalues of the stiffness matrix

λ_{1} |
λ_{2} |
λ_{3} |
λ_{4} |
λ_{5} |
λ_{6} |
---|---|---|---|---|---|

55.893 GPa | 67 GPa | 68 GPa | 112.58 GPa | 130.08 GPa | 340.45 GPa |

### Variations of the elastic moduli

Young's modulus | Linear compressibility | Shear modulus | Poisson's ratio | ||||||
---|---|---|---|---|---|---|---|---|---|

E_{min} | E_{max} |
β_{min} | β_{max} | G_{min} | G_{max} |
ν_{min} | ν_{max} | ||

Value | 134.25 GPa | 190.81 GPa | 1.8549 TPa^{–1} | 3.882 TPa^{–1} | 55.934 GPa | 68 GPa | 0.22684 | 0.34728 | Value |

Anisotropy | 1.421 | 2.0929 | 1.216 | 1.5309 | Anisotropy | ||||

Axis | 0.8605 0.5095 0.0000 |
0.0000 0.0000 1.0000 |
0.0000 0.0000 1.0000 |
0.8984 0.4391 0.0000 |
0.0407 0.9992 -0.0000 |
0.0000 0.0000 1.0000 |
-0.5431 0.8397 0.0000 |
-0.0001 -0.0001 1.0000 |
Axis |

-0.9992 0.0407 0.0000 |
-1.0000 0.0000 0.0000 |
0.0000 -0.0000 1.0000 |
-0.8764 -0.4816 -0.0001 |
Second axis |

## Spatial dependence of Young's modulus

Young's modulus in (xy) plane

Young's modulus in (xz) plane

Young's modulus in (yz) plane

## Spatial dependence of linear compressibility

linear compressibility in (xy) plane

linear compressibility in (xz) plane

linear compressibility in (yz) plane

## Spatial dependence of shear modulus

Shear modulus in (xy) plane

Shear modulus in (xz) plane

Shear modulus in (yz) plane

## Spatial dependence of Poisson's ratio

Poisson's ratio in (xy) plane

Poisson's ratio in (xz) plane

Poisson's ratio in (yz) plane